Norwich's second-half pressure finally told as Simeon Jackson's injury-time header denied Fulham only their second away win of the season.
Orlando Sa wrapped a curling effort around John Ruddy after seven minutes and would have had a second but for Kyle Naughton's goal-line clearance.
Clint Dempsey hit the woodwork with a header for Fulham, but the hosts pressed forward after the break.
Naughton rattled the bar before Jackson nodded in Elliott Bennett's cross.
The result ensures Norwich finish 2011 in the top half of the Premier League and, although Blackpool occupied a similar position at the same time last year before being relegated in May, the Canaries' fighting spirit will give them hope of another top-flight campaign.
Having fallen behind to Sa's early effort, the aerial route always seemed the likeliest to deliver an equaliser for a home side that has scored more headed goals than any other in the division.
During a late bombardment of the visitors' box, goalkeeper David Stockdale saved sharply from Zak Whitbread's header and was then relieved to see Grant Holt's effort clear the bar after the striker clambered over Phillippe Senderos.
But Fulham's resolve was finally broken as Bennett swept over an inviting centre in the fourth minute of injury time and fellow substitute Jackson glanced into the far corner to spark wild celebrations.
Visiting manager Martin Jol will have been disappointed with just a point after a vibrant attacking display in the first half.
Neither Bobby Zamora nor Andrew Johnson travelled to East Anglia amid speculation that the strikers, who have not played since the 5-0 defeat by Manchester United on 21 December, could leave in January.
In their absence, Sa led the line well and celebrated his opener with his boss after swivelling free of Whitbread following good work from Moussa Dembele.
The 24-year-old almost added to his first Premier League goal after being sent through by Kerim Frei but although his shot beat Ruddy it was booted clear by Naughton.
Norwich rallied briefly with Bradley Johnson's effort deflecting narrowly wide off Brede Hangeland before Whitbread's header was clawed on to the woodwork by Fulham keeper David Stockdale.
But the Norwich defence creaked as the visitors advanced with purpose and Clint Dempsey's close-range header rattled the bar before the lively Frei warmed Ruddy's palms with a solid strike.
Wesley Hoolahan blazed over the top and the hosts had a half-hearted penalty shout waved away towards the end of the half, but it was little surprise when Canaries boss Paul Lambert threw on striker Holt.
The substitute provided a much-needed platform for the home side's attacks and only Hoolahan's poor first touch denied him a shooting chance from Steve Morison's neat cut-back.
The Canaries continued to press as Naughton cut inside and shuddered the bar with a right-foot shot while Anthony Pilkington thumped a 20-yard drive just over the top.
Andrew Surman had Stockdale scampering in pursuit of his low drilled effort, before Lambert made his second important change to his frontline.
Jackson came on for Morison and had already stretched Stockdale with a swerving effort before getting the telling touch in the game's dying moments.